The insertion and deletion algorithms described in section 7.4.1 have to be modified in the case of a condensed IP-table I'(R,a). They have to incorporate the notion of timepoints having been collapsed into one timepoint, i.e. that an interval [r.ts,r.te] might not have its start- and endpoints within the set V'(R,a). Therefore, we have to determine the timepoints t'js and t'je of V'(R,a) which represent r.ts and r.te respectively. In the case of r being inserted into R, one has to include r.te if r's timestamp falls partly or entirely beyond the current value of t'N'. Such a situation is characterised by r.te > t'N'. Similarly, r.te can be removed on deletion of r if there are no more intervals ending at t'N', i.e. if all intervals have ended before, at t'N'-1. At the opposite end, we can remove t'1 if there are no more intervals starting at t'1. Apart from these modifications, the insertion and deletion algorithms remain the same. They are shown in figures 7.12 and 7.13.
From these algorithms it is apparent that condensed IP-tables can not be maintained without a loss of accuracy. Basically, once the condensation of timepoints has been performed, one cannot control that a condensed timepoint t'j still represents a original timepoints of V(R). After several insertions or deletions this number might have changed. The only control that can be performed is the one over t'1 and t'N' which can be removed in case that they become obsolete. Therefore one can expect that the quality of information provided by a condensed IP-table decreases with an increasing amount of updates. This suggests that condensed IP-table might need to be recomputed periodically, in particular if insertions or deletions concentrate on specific parts of the timeline.